When tuning a guitar, a musician plucks a string and listens to its tone. But if there is construction noise nearby, hearing the pure sound is difficult. An atom also has its own 'tone': the frequency at which it absorbs or emits light. For potassium-40, this tone was hard to measure precisely because magnetic fields interfered, shifting the frequency like construction noise drowning out the string's sound.
Physicists came up with a clever trick: instead of fighting the noise, they chose two transitions that barely respond to magnetic fields. It is like a musician playing on a string that is deaf to construction noise. By measuring the frequencies of these two transitions and their difference, one can calculate the desired constant without even knowing what the field was.
The result is a hyperfine constant A = −h × 285.730536(2) MHz. Previously it was known to 2.4 kHz, now to 2 Hz. This is like a musician finally hearing the pure tone of the string without interference. Now this tone can be used as a reference for tuning other instruments, that is, for calibrating magnetic fields and studying atomic interactions.
The natural abundance of 40K is only 0.0117%: out of a million potassium atoms, just 117 are this isotope. To obtain millions of atoms for experiments, costly enrichment is required.